Molecular Orbitals - Delocalized Chemical Bonding - Introduction - March's Advanced Organic Chemistry: Reactions, Mechanisms, and Structure, 7th Edition (2013)

March's Advanced Organic Chemistry: Reactions, Mechanisms, and Structure, 7th Edition (2013)

Part I. Introduction

Chapter 2. Delocalized Chemical Bonding

Although the bonding of many compounds can be adequately described by a single Lewis structure (Sec. 1.F), this is insufficient for many other compounds. Such compounds contain one or more bonding orbitals that are not restricted to two atoms, but rather they are spread out over three or more atoms. Such bonding is said to be delocalized.1 In other words, the bonding electrons are dispersed over several atoms rather than localized on one atom. This Chapter 2 will discuss those compounds that must be represented in this way.

The two chief general methods of approximately solving the wave equation, discussed in Chapter 1, are also used for compounds containing delocalized bonds.2 In the valence bond method, several possible Lewis structures (called canonical forms) are drawn, and the molecule is taken to be a weighted average of them. Each Ψ in Eq. (1–3), represents one of these structures. Therefore,

equation

is the representation of a real structure as a weighted average of two or more canonical forms, which is called resonance. For benzene the canonical forms are drawn as 1 and 2. Double-headed arrows (↔) are used to indicate resonance. When the wave equation is solved, it is found that the energy value obtained by equal participation of 1 and 2 is lower than that for 1 or 2 alone. If 35 (called Dewar structures) are also considered, the value is lower still. According to this method, 1 and 2 contribute 39% each to the actual molecule and the others 7.3% each.3 The carbon–carbon bond order is 1.463 (not 1.5, which would be the case if only 1 and 2 contributed).

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In the valence bond method, the bond order of a particular bond is the sum of the weights of those canonical forms in which the bond is double plus 1 for the single bond that is present in all of them.4 Thus, according to this picture, each C–C bond is not halfway between a single and a double bond but is somewhat less. The energy of the actual molecule is obviously less than that of any one Lewis structure, since otherwise it would have one of those structures. The difference in energy between the actual molecule and the Lewis structure of lowest energy is called the resonance energy. Of course, the Lewis structures are not real, and their energies can only be estimated. Resonance in benzene is possible by overlap of the p orbitals, orthogonal to the plane of carbon and hydrogen atoms. This resonance is associated with the aromatic π-cloud. Figure 2.1 shows the planar σ-bond framework of benzene, with the overlapping p-orbitals forming the aromatic π-cloud. Figure 2.1 also shows the electron potential map of benzene. Note the darker area above the middle of the ring that corresponds to high electron density, consistent with the high electron density of the aromatic π-cloud.

Fig. 2.1 (a) Traditional drawing of the overlapping p orbitals that comprise the π-cloud in benzene. (b) The electrostatic potential map of benzene, indicating the high concentration of electron density above and below the plane of the atoms, but in the center of the six-membered ring, consistent with the aromatic cloud.

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2.A. Molecular Orbitals

While the resonance picture is often used to describe the structure of molecules, as structures become more complicated (e.g., naphthalene and pyridine), quantitative valence bond calculations become much more difficult. Therefore, the MO method is used much more often for the solution of wave equations.5 Examination of benzene by this method (qualitatively) shows that each carbon atom, being connected to three other atoms, uses sp2 orbitals to form σ bonds, so that all 12 atoms are in one plane. This method shows that each carbon has a remaining p orbital that contains one electron, and each orbital can overlap equally with the two adjacent p orbitals. This overlap of six orbitals (see Fig. 2.2) produces six new orbitals, and the three lower energy orbitals are bonding. These three (called π orbitals) all occupy approximately the same space.6 One of the three is of lower energy than the other two, which are degenerate. They each have the plane of the ring as a node and so are in two parts, one above and one below the plane. The two orbitals of higher energy also have another node. The six electrons that occupy this torus-shaped cloud are called the aromatic sextet. A torus-shaped object is essentially a doughnut-shaped object. According to this explanation, the symmetrical hexagonal structure of benzene is caused by both the σ bonds and the (orbitals. Based on MO calculations, this symmetry is probably caused by the σ framework alone, and that the (π system would favor three localized double bonds.6 The carbon–carbon bond order for benzene, calculated by the MO method, is 1.667.7

Fig. 2.2 The molecular orbitals of benzene, showing the three bonding orbitals, as generated by Spartan.10, v.1.0.1.

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For planar unsaturated molecules that are aromatic, many MO calculations have been made by treating the σ and π electrons separately. It is assumed that the σ orbitals can be treated as localized bonds and the calculations involve only the π electrons. The first such calculations were made by Hückel, and such calculations are often called Hückel molecular orbital (HMO) calculations.8 Because electron–electron repulsions are either neglected or averaged out in the HMO method, another approach, the self-consistent field (SCF), or Hartree–Fock, method, was devised.9 Although these methods give many useful results for planar unsaturated and aromatic molecules, they are often unsuccessful for other molecules. It would obviously be better if all electrons, both σ and π, could be included in the calculations. The development of modern computers has now made this possible.10 Many such calculations have been made11 using a number of methods, among them an extension of the Hückel method 12 and the application of the SCF method to all valence electrons.13

One type of MO calculation that includes all electrons is called ab initio.14 Despite the name (which means “from first principles”) this type does involve some assumptions. Treatments that use certain simplifying assumptions (but still include all electrons) are called semiempirical methods.15 One of the first of these was called CNDO (Complete Neglect of Differential Overlap),16 but as computers have become more powerful, this has been superseded by more modern methods, including MINDO/3 (Modified Intermediate Neglect of Differential Overlap),17 MNDO (Modified Neglect of Diatomic Overlap),17 and AM1 (Austin Model 1), all of which were introduced by M.J. Dewar et al.18 There is also the PM3, or Parameterized Model number 3, which the same formalism and equations as the AM1 method, but AM1 takes some of the parameter values from spectroscopic measurements, whereas PM3 treats them as optimizable values.19 Semiempirical calculations are generally regarded as less accurate than ab initio methods,20 but are much faster and cheaper.21 Note that modern computers are capable of completing >3 billion calculations per second, which makes MO calculations practical in modern organic chemistry.

Molecular orbital calculations, whether by ab initio or semiempirical methods, can be used to obtain structures (bond distances and angles), energies (e.g., heats of formation), dipole moments, ionization energies, and other properties of molecules, ions, and radicals: not only of stable ones, but also of those so unstable that these properties cannot be obtained from experimental measurements.22 Many of these calculations have been performed on transition states (Sec. 6.D). This is the only way to get this information, since transition states are not directly observable. Of course, it is not possible to check data obtained for unstable molecules and transition states against any experimental values, so that the reliability of the various MO methods for these cases is always a question. However, confidence in them increases when (1) different MO methods give similar results, and (2) a particular MO method works well for cases that can be checked against experimental methods.23

Both the valence bond and MO methods show that there is delocalization in benzene. For example, each predicts that the six carbon–carbon bonds should have equal lengths, which is true. Since each method is useful for certain purposes, one or the other will be used as appropriate. Recent ab initio, SCF calculations confirm that the delocalization effect acts to strongly stabilize symmetric benzene, consistent with the concepts of classical resonance theory.24It is known that substituents influence the extent of resonance.25